Rob Twiss asked me to post this 'cos he has problems posting from his own PC.

Colleagues,

	In the interest of clear communication I would like to contribute
several points to the pure shear/simple shear discussion.

	1)  In their rigorous definitions, pure shear and simple shear are
both constant-volume, two dimensional strains:  add any volumetric
deformation or deformation in the third dimension and technically it is no
longer a pure shear or a simple shear.  These really are incredibly
restricted geometries of strain to use for describing geologic deformation.

	2)  A more general term is 'pure strain', for which the principal
axes of strain remain constant in orientation relative to the reference
coordinate system, also called 'irrotational strain'.  The reference axes,
however, are not uniquely defined, so this description is dependent on the
definition of a reference frame, which for geological purposes is often not
very useful.

	3)  Coaxial and non-coaxial deformation are probably the best
generalizations of what people often mean when they talk of pure and simple
shear in a geological context.  If finite and incremental strain axes
remain parallel throughout a deformation, it is coaxial; if they do not
remain parallel, it is non-coaxial.  Thus pure shear is coaxial; simple
shear is non-coaxial.  But coaxial deformation is more general than pure
shear, and non-coaxial deformation is more general than simple shear.
Coaxial and non-coaxial are useful characterizations of geological
deformations, because the reference frames are internally defined by the
deformation itself.

	4)  We must not assume that the ideas of principal strain and
principal stress can be used interchangably.  This is a horse some may
recognize as one I love to flog, especially with regard to fault-slip
inversions (Twiss & Unruh, 1998, Jour. Geophys. Res.
v.103(B6):12205-12222).  But similar arguments apply to other situations.
What we see recorded in rocks is STRAIN, and the inference of the
orientations and relative magnitudes of the principal strains or principal
incremental strains (strain rates) can only be interpreted as reflecting
the principal stresses if the rock is rheologically linear and mechanically
isotropic, neither of which is a very good bet, I suspect.  Since the
relation of strain to stress is subject to considerable debate, we should
restrict our discussions to strain.
	The only fabric elements I know of that are directly related to
stress are certain paleopiezometers such as dynamically recrystallized
grain size, subgrain size, and dislocation density.  These reflect the
magnitude of the differential stress (maximum principal stress difference),
but not the orientations of the principal stresses.

	5)  It is important in these discussions to keep the concept of
scale in mind.  All continuum descriptions of deformation (such as strain)
rely on an averaging of motions over volumes that are large with respect to
the inherent heterogeneities of real materials.  Even the description of
the macroscopic flow of water or air requires averaging at least over
volumes that are large relative to the atomic heterogeneities of these
materials.
	In rocks, we recognize that heterogeneities exist at a wide variety
of scales, but to discuss whether a strain is homogeneous or heterogeneous,
we must define the scale at which the strain is considered (hand sample?  1
km?  100 km?) and the scale of heterogeneities in the rock over which we
can and cannot average.  A heterogeneity on the scale of a mineral grain or
a clast will have no bearing on the geometry of strain measured at the
scale of a diapiric or orogenic flow.

	That's certainly enough for one message.

	Cheers,

Rob Twiss

Robert J. Twiss                         Internet: [log in to unmask]
Geology Department                      telephone: (530) 752-1860
University of California at Davis       FAX:       (530) 752-0951
One Shields Ave.
Davis, CA 95616-8605, USA

Prof Tim Bell
School of Earth Sciences
James Cook University
Townsville
QLD 4811
Australia
ph: +61 7 47814766
fax: +61 7 47251501
email: [log in to unmask]




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